Do the fastest or slowest moving molecules break away from the surface of the liquid water to form water vapor?

When you heat up a substance (be it a solid, liquid, or gas), you are adding thermal energy to the substance. This energy is disseminated to the individual molecules in the substance, like water molecules when you heat up a pan of water on the stove. Water molecules can rotate, their bonds can vibrate, and they can collide with one another. The more energy the water molecules have, the more they move and collide with one another. Once you heat the water up to 100 degrees Celsius, the fastest moving water molecules at the surface leave the bulk liquid and become gas molecules. Once they leave the bulk liquid, there is more energy and room available for slower moving molecules to move faster and reach the surface. So the answer to your question is that the fastest moving molecules break away to form water vapor.